FIG. 1 illustrates a traditional engineering design process for designing a composite structure. Such a process will typically consist of some iterative analysis 1 and redesign 2 in which engineering analysis may play a role in suggesting design updates. The iterative re-design process is typically terminated once a satisfactory design is achieved. A satisfactory design could be a minimum weight design satisfying a number of structural performance requirements and composite layout design rules.
Gradient-based numerical optimization offers techniques that allow a systematic search for an optimum design that simultaneously will satisfy multiple design requirements. Such numerical optimization methods are available for solving optimization problems with 1,000's of design variables and 1,000,000's of constraint equations. The solution process is a systematic approach, with a process flow as illustrated in FIG. 2.
The first difference one notices when comparing the processes in FIGS. 1 and 2 is the use of mathematical terms such as sensitivity analysis 3 and convergence 4. This reflects that the treatment of the design problem has been turned into a mathematical problem, which is solved using mathematical programming techniques. It is this mathematical and very systematic treatment of the design problem that makes it possible to solve design optimization problems with 1000's of design variables and 1,000,000's of constraints.
Solving an optimization problem via a gradient-based optimization search process, such as the one illustrated in FIG. 2, requires a number of steps to be performed.
Firstly the current design is analyzed in step 5. Typically in structural optimization a designer is interested in minimizing weight, whilst satisfying a number of strength, buckling and other structural design requirements. The analysis task in step 5 would in this case consist of evaluating current values for an optimization objective function (weight) and constraints (buckling, strength and other structural requirements).
Secondly a so-called design sensitivity analysis is performed in step 3. The design sensitivity analysis consists of a calculation of partial derivatives of the optimization objective and constraint functions with respect to design variable changes. In less mathematical terms—design sensitivities are numbers that tell/predict how the optimization objective and constraint functions will change when design variables are changed. Design sensitivities may be calculated either by analytical differentiation or by numerical approximations such as finite differences.
Having calculated current values of optimization objective functions and constraint functions in step 5, and having calculated design sensitivities in step 3, it is possible to build an approximate design model that predicts the values of both the objective function and all constraint functions after a simultaneous change of multiple design variables. The design models are often built utilizing mathematical approximation schemes that allow an efficient solution of the mathematically formulated design problem. Possibly the simplest approximation scheme is a simple linear model or Taylor series expansion. FIG. 3 shows how a linear approximation 6 can be constructed around a current design point 7. Such a linear prediction would be a reasonable estimation of true function behaviour if we do not take steps which are too large.
Numerical optimization processes may be seen to work by substituting the solution of a “non-linear” optimization problem by the solution of a sequence of approximating optimization problems. Having formulated the approximate design problem a mathematical programming algorithm is used to solve the optimization problem and determine an optimum update of design variables. After this the cycle can start again with another analysis and sensitivity analysis. Typically software for constructing approximate design problems and for solving such problems are integrated into a single package.
Convergence checks (indicated at 4 in FIG. 2) simply consist of checks that tell if the optimization solution process has stopped making progress, if the design has stabilized and if all design constraints are satisfied.
Consider now a method of designing a composite panel, the panel comprising a plurality of zones, each zone comprising a plurality of plies of composite material, each ply in each zone having a respective orientation angle, and some of the plies running continuously between adjacent zones.
Each zone has a laminate ply percentage for each orientation angle which represents the percentage of plies in that zone having that particular orientation angle. Ply continuity is a measure of how many plies run continuously between a given pair of adjacent zones. That is, a pair of zones where all the plies run continuously between the zones have a high degree of ply continuity, whereas a pair of zones where some of the plies are broken or discontinued at the junction between the zones have a low degree of ply continuity.
Clearly if the thickness between zones is varying it will be necessary to remove plies or introduce additional plies. It would be desirable to provide an optimisation formulation which not only allows laminate thickness and laminate ply percentages to be varied across the panel, but which also impose constraints that will maximise ply continuity between adjacent zones.